What's New -  August 2013

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August 13, 2013:  The Challenging Math Teasers program posted today implements  three problems of the 100 presented in the "Challenging Mathematical Teasers" book by J.A.H. Hunter  and published by Dover Publications. The puzzles generally require math techniques beyond simply solving an algebraic equation or two. The three presented here were chosen randomly are easily amenable to programmed solutions (and have relatively short descriptions :>).  By the way, the above book link to Amazon offers a number of good used copies for $0.01 + $3.99 shipping,  if you reside in the U.S. and act quickly.

The program is a one day effort while taking a break from the "Find All Polygons" program I have been wrestling with for the past two weeks.   Who knew polygons could be so hard to find?

I placed this program in the Math Topics section of DFF but also indexed it under Delphi Techniques and Beginners categories since it does illustrate some useful number manipulation techniques with less than 20 source code statements to handle each of the 3 problem buttons.  

August 22, 2013:

Simple case: How many polygons can you find embedded here?

After a month of on-and-off effort, here is Find All Polygons, a program to look for polygons, closed figures formed from connected straight line segments.  According to Wikipedia, "Polygon" is derived from Greek with literal meaning "many corners".  Typically, but not always,  the number of corners, (vertices), equals the number sides (edges).  I learned much about them in the course of writing this program including the many ways that  arbitrary closed sets of  of lines may not be valid polygons.  The program analyzes several different sample figures including one from which several hundred polygons can be selected.  Needless to say, I have not examined all of them so there still may be polygons missed or non-polygons selected.  Let me know if you find errors.  
 

August 26, 2013:

16 "Primitive" triangles, (out of 46 total!)

 Find All Polygons, Version 3.2 posted today is better than last week's posting at finding all polygons at a given search level.  When I added the figure from our "How Many Triangles?" program to this program, I realized that some of the  interior nodes (created when interior lines intersect) were not being examined during the polygon search.  The problem is corrected today.  The easily checked polygon counts (the Tennis problem's rectangle counts,  the Triangles problem's triangle counts, and the the primitive counts for any figure are now correct.  (Total rectangle and triangle counts are found by limiting "Max Search Depth" values to 5 and 4 respectively.)